Multiple pulse NMR spin-echo techniques are proposed to obtain direct measurements of translational diffusion coefficients and their tensoral properties in bilayer membranes. By applying NMR techniques which have been developed for diffusion studies in liquid crystals, direct measurements of the lipid self-diffusion tensor are proposed in addition to the diffusion tensor of other molecules restricted by the bilayer. The experiments involve multilayers of various lipids in the planar lamellar and vesicle form.